how can I get wires through the swing arm part of a lamp?

Make sure that the cable you intend to use is exactly the same thickness as the old stuff. You may be able to pass a thin length of welding wire through the lamp and solder the new wire on to the end to help pulling it through, but be careful that any sharp edges inside don't shred the insulation. If all else fails, you may have to run the new wire externally.

John
March 2009